The tree of good semigroups in ℕ² and a generalization of the Wilf conjecture

2019/07/02 by Maugeri, Nicola, Zito, Giuseppe
#13A18 #13H99 #14H99 #20M25 #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1907.01315

Abstract

In this work, we study good semigroups of ℕⁿ introducing the definition of length and genus for these objects. We show how to count the local good semigroup with a fixed genus. Furthermore, we study the relationships of these concepts with other ones previously defined in the case of good semigroups with two branches.

Related

• Embedding dimension of a good semigroup
• Arf good semigroups
• Arf good semigroups with fixed genus
• Trimming the numerical semigroups tree to probe Wilf's conjecture to higher genus
• Towards a Better Understanding of the Semigroup Tree